Question: Evaluate the definite integral. $\int^{-1}_{1}3e^x\,dx = $ Choose 1 answer: Choose 1 answer: (Choice A) A $3e-3e^{-1}$ (Choice B) B $3e^{-1}-3e$ (Choice C) C $-3e^{-1}+1$ (Choice D) D None of the above
Solution: First, use the exponent rule: $\begin{aligned}\int^{-1}_{1}3e^x\,dx =~3e^x\Bigg|^{-1}_{{1}}\end{aligned}$ Second, plug in the limits of integration: $(3e^{{-1}})-(3e^{{1}}) = 3(e^{-1}-e)$. The answer: $\int^{-1}_{1}3e^x\,dx~=~3(e^{-1}-e)$